Real analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908480257916928 |
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| author | Son, Miri |
| author_facet | Son, Miri |
| contents | We classify real-analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds of dimension m for $3\leq n\leq m\leq2n-3$, which extends Fisher--Melnick's work for $\mathrm{SL}(n,\mathbb{R})$-actions on closed n-manifolds. Additionally, we classify smooth $\mathrm{SL}(n,\mathbb{R})$-actions on closed m-manifolds that are fixed-point free. As a corollary, we obtain the density or non-density of structural stability of fixed-point free $\mathrm{SL}(n,\mathbb{R})$-actions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Real analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds Son, Miri Dynamical Systems Differential Geometry Geometric Topology We classify real-analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds of dimension m for $3\leq n\leq m\leq2n-3$, which extends Fisher--Melnick's work for $\mathrm{SL}(n,\mathbb{R})$-actions on closed n-manifolds. Additionally, we classify smooth $\mathrm{SL}(n,\mathbb{R})$-actions on closed m-manifolds that are fixed-point free. As a corollary, we obtain the density or non-density of structural stability of fixed-point free $\mathrm{SL}(n,\mathbb{R})$-actions. |
| title | Real analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds |
| topic | Dynamical Systems Differential Geometry Geometric Topology |
| url | https://arxiv.org/abs/2508.04499 |